Assigning bars to closest building using PostGIS?

Question

I'm using PostGIS and OpenStreetMap, I tried to assign some bars to the nearest building from themselves I based myself on an example, see: link You can see below picture that resulted from below script. Where its circled in red the location of each bar is incorrect. Its not showing what I need to see. The selected location of the bar is not in front of it.

SELECT DISTINCT ON (b.osm_id) b.osm_id as osm_bar, a.osm_id as osm_building, ST_Distance(a.way, b.way)  as distance
FROM buildings a, bar_not_assigned b  
WHERE ST_DWithin(a.way, b.way, 10) 
ORDER BY b.osm_id, a.osm_id, ST_Distance(a.way, b.way);

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When i used the script in this post link I got this result:

select poly.osm_id
from (select osm_id, way from buildings) poly
cross join lateral
  (select osm_id, way
   from bar_not_assigned pt
   where st_dwithin(pt.way, poly.way, 10)
   order by pt.way <-> poly.way limit 1) pts;

I changed limit to 1 to have one bulding for each bar, but does not work.

Answer 1

select temp.bar_non_assigne.*, closest.batiment_id
from temp.bar_non_assigne
cross join lateral
    (select source.batiment.osm_id as batiment_id, 
     temp.bar_non_assigne.osm_id as bar_id, 
     st_distance(source.batiment.way, temp.bar_non_assigne.way) as distance
     from source.batiment
     where st_dwithin(source.batiment.way, temp.bar_non_assigne.way, 10)
     order by source.batiment.way <-> temp.bar_non_assigne.way
     limit 1) as closest
 where temp.bar_non_assigne.osm_id = closest.bar_id;